9. Too little care for rigor. It is notoriously easy to find "bugs" in
algorithms for symbolic computation. To make matters worse, these errors are often regarded as of no significance by their authors, who plead that the result returned is true "except on a set of measure zero", without explicitly naming the set involved. The careful determination, nay, even proof, of precisely which conditions under which a result is true is essential for building the structure of mathematics so that one can depend on it. The QED system will support the development of symbolic algebra programs in which formal proofs of correctness of derivations are provided, along with the precise statement of conditions under which the results are true. _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer |
Tim: The notion of a "set of measure zero" could just be hiding the fact that they just don't know what it is ;) On to something less humorous: I am about to up grade my primary system to a MAC device with Windows 10 and Linux as alternate boots. This is part of a project I've been contemplating to try to develop a "dual" to AXIOM that would capture the experience of a "developer" who tries to build a system from scratch. "Build" means taking the algebra code and compiling each component, one by one, until a full AXIOM system has achieved. Gene On 12/22/2018 5:17 PM, Tim Daly wrote: > 9. Too little care for rigor. It is notoriously easy to find "bugs" in > algorithms for symbolic > computation. To make matters worse, these errors are often regarded as > of no significance > by their authors, who plead that the result returned is true "except > on a set of measure > zero", without explicitly naming the set involved. The careful > determination, nay, even > proof, of precisely which conditions under which a result is true is > essential for building > the structure of mathematics so that one can depend on it. The QED > system will support > the development of symbolic algebra programs in which formal proofs of > correctness of > derivations are provided, along with the precise statement of > conditions under which the > results are true. > > _______________________________________________ > Axiom-developer mailing list > [hidden email] > https://lists.nongnu.org/mailman/listinfo/axiom-developer > _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer |
I am rebuilding the Axiom compiler to support the algorihmic
proof technology. It is a difficult problem and I still have much to learn. However, I think that we need to connect the "proof" side of computational mathematics with computer algebra computational mathematics. After nearly 3 years taking courses at CMU I think I see how it will succeed. Whether *I* am capable of doing it is still an open question :-) Tim On 12/23/18, Eugene Surowitz <[hidden email]> wrote: > > Tim: > > The notion of a "set of measure zero" could just > be hiding the fact that they just don't know what it is ;) > > On to something less humorous: > > I am about to up grade my primary system to a MAC device > with Windows 10 and Linux as alternate boots. > This is part of a project I've been contemplating > to try to develop a "dual" to AXIOM that would capture the > experience of a "developer" who tries to build a system > from scratch. "Build" means taking the algebra code > and compiling each component, one by one, until a full > AXIOM system has achieved. > > Gene > > > > On 12/22/2018 5:17 PM, Tim Daly wrote: >> 9. Too little care for rigor. It is notoriously easy to find "bugs" in >> algorithms for symbolic >> computation. To make matters worse, these errors are often regarded as >> of no significance >> by their authors, who plead that the result returned is true "except >> on a set of measure >> zero", without explicitly naming the set involved. The careful >> determination, nay, even >> proof, of precisely which conditions under which a result is true is >> essential for building >> the structure of mathematics so that one can depend on it. The QED >> system will support >> the development of symbolic algebra programs in which formal proofs of >> correctness of >> derivations are provided, along with the precise statement of >> conditions under which the >> results are true. >> >> _______________________________________________ >> Axiom-developer mailing list >> [hidden email] >> https://lists.nongnu.org/mailman/listinfo/axiom-developer >> > _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer |
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